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<a name="Fitting-linear-regression-example"></a>
<div class="header">
<p>
Next: <a href="Fitting-multi_002dparameter-linear-regression-example.html#Fitting-multi_002dparameter-linear-regression-example" accesskey="n" rel="next">Fitting multi-parameter linear regression example</a>, Up: <a href="Fitting-Examples.html#Fitting-Examples" accesskey="u" rel="up">Fitting Examples</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Simple-Linear-Regression-Example"></a>
<h4 class="subsection">38.8.1 Simple Linear Regression Example</h4>

<p>The following program computes a least squares straight-line fit to a
simple dataset, and outputs the best-fit line and its
associated one standard-deviation error bars.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdio.h&gt;
#include &lt;gsl/gsl_fit.h&gt;

int
main (void)
{
  int i, n = 4;
  double x[4] = { 1970, 1980, 1990, 2000 };
  double y[4] = {   12,   11,   14,   13 };
  double w[4] = {  0.1,  0.2,  0.3,  0.4 };

  double c0, c1, cov00, cov01, cov11, chisq;

  gsl_fit_wlinear (x, 1, w, 1, y, 1, n, 
                   &amp;c0, &amp;c1, &amp;cov00, &amp;cov01, &amp;cov11, 
                   &amp;chisq);

  printf (&quot;# best fit: Y = %g + %g X\n&quot;, c0, c1);
  printf (&quot;# covariance matrix:\n&quot;);
  printf (&quot;# [ %g, %g\n#   %g, %g]\n&quot;, 
          cov00, cov01, cov01, cov11);
  printf (&quot;# chisq = %g\n&quot;, chisq);

  for (i = 0; i &lt; n; i++)
    printf (&quot;data: %g %g %g\n&quot;, 
                   x[i], y[i], 1/sqrt(w[i]));

  printf (&quot;\n&quot;);

  for (i = -30; i &lt; 130; i++)
    {
      double xf = x[0] + (i/100.0) * (x[n-1] - x[0]);
      double yf, yf_err;

      gsl_fit_linear_est (xf, 
                          c0, c1, 
                          cov00, cov01, cov11, 
                          &amp;yf, &amp;yf_err);

      printf (&quot;fit: %g %g\n&quot;, xf, yf);
      printf (&quot;hi : %g %g\n&quot;, xf, yf + yf_err);
      printf (&quot;lo : %g %g\n&quot;, xf, yf - yf_err);
    }
  return 0;
}
</pre></div>

<p>The following commands extract the data from the output of the program
and display it using the <small>GNU</small> plotutils <code>graph</code> utility, 
</p>
<div class="example">
<pre class="example">$ ./demo &gt; tmp
$ more tmp
# best fit: Y = -106.6 + 0.06 X
# covariance matrix:
# [ 39602, -19.9
#   -19.9, 0.01]
# chisq = 0.8

$ for n in data fit hi lo ; 
   do 
     grep &quot;^$n&quot; tmp | cut -d: -f2 &gt; $n ; 
   done
$ graph -T X -X x -Y y -y 0 20 -m 0 -S 2 -Ie data 
     -S 0 -I a -m 1 fit -m 2 hi -m 2 lo
</pre></div>


<hr>
<div class="header">
<p>
Next: <a href="Fitting-multi_002dparameter-linear-regression-example.html#Fitting-multi_002dparameter-linear-regression-example" accesskey="n" rel="next">Fitting multi-parameter linear regression example</a>, Up: <a href="Fitting-Examples.html#Fitting-Examples" accesskey="u" rel="up">Fitting Examples</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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